"David Park" <djmp at earthlink.net> wrote in message
news:<c07p9h$kmc$1 at smc.vnet.net>...
>
> I'm always interested in Mathematica techniques for manipulating and simplifying algebraic expressions. I came across the following problem, which I was only able to do with a fair amount of difficulty.
>
> expr = x*y*(-(z^2/(r^2*(x^2 + y^2))) - 1/(r*(k + r)) + 1/(x^2 + y^2))
>
> where
>
> r^2 == x^2 + y^2 + z^2
>
> reduces to
>
> (k*x*y)/(r^2*(k + r))
>
> I wonder if anyone can show an elegant or short method to do the simplification?
Together[expr /. x^2+y^2 -> r^2-z^2] gets it for me.